\newproblem{lay:1_5_13}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.5.13}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Suppose the solution set of a certain system of linear equations can be described as $x_1=5+4x_3$, $x_2=-2-7x_3$, with $x_3$ free.
	Use vectors to describe this set as a line in $\mathbb{R}^3$.
}
{
  % Solution
	The general solution of the system of linear equations is
	\begin{center}
		$\mathbf{x}=\begin{pmatrix}5+4x_3\\-2-7x_3\\x_3\end{pmatrix}=\begin{pmatrix}5\\-2\\0\end{pmatrix}+x_3\begin{pmatrix}4\\-7\\1\end{pmatrix}$
	\end{center}
	This is a line that passes through the point $\mathbf{x}_0=(5,-2,0)$ and whose direction vector is $(4,-7,1)$.
}
\useproblem{lay:1_5_13}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
